High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures. We test the method numerically by analyzing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test. The method paves a road for experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.

高阶量子非线性是先进量子技术实现具有连续变量大信息容量的通用量子处理的重要前提。悬浮光机械是一个由精确控制的镊子光束驱动介电粒子运动的领域，能够通过机械运动的工程潜在景观获得所需的非线性。重要的是，要实现非线性量子效应，必须抑制由力学自由运动和热退相干引起的演化。以此目的，我们设计了一种将高度非线性电势频闪应用于机械振荡器的方法，该方法导致运动量子非高斯状态表现出非经典的负 Wigner 函数并压缩机械正交的非线性组合。我们通过对悬浮光力学相关实验参数的高度不稳定立方势分析，对该方法进行了数值测试，证明了其可行性，并提出了实验测试。该方法为通过非线性光力将机械振荡器的基态瞬时转换为适用的非经典态的实验铺平了道路。并提出实验测试。该方法为通过非线性光力将机械振荡器的基态瞬时转换为适用的非经典态的实验铺平了道路。并提出实验测试。该方法为通过非线性光力将机械振荡器的基态瞬时转换为适用的非经典态的实验铺平了道路。